wp.mrt2arm {WebPower}

Statistical Power Analysis for Multisite Randomized Trials with 2 Arms

Description

Multisite randomized trials (MRT) are a type of multilevel design for the situation when the entire cluster is randomly assigned to either a treatment arm or a control arm (Liu, 2013). The data from MRT can be analyzed in a two-level hierarchical linear model, where the indicator variable for treatment assignment is included in first level. If a study contains multiple treatments, then multiple indicators will be used. This function is for designs with 2 arms (i.e., a treatment and a control). Three types of tests are considered in the function: (1) The "main" type tests treatment main effect; (2) The "site" type tests the variance of cluster/site means; and (3) The "variance" type tests variance of treatment effects. Details leading to power calculation can be found in Raudenbush (1997) and Liu (2013).

Usage

wp.mrt2arm(n = NULL, f = NULL, J = NULL, tau00 = NULL, tau11 = NULL,
  sg2 = NULL, power = NULL, alpha = 0.05, alternative = c("two.sided",
  "one.sided"), type = c("main", "site", "variance"), interval = NULL)

Arguments

n

Sample size. It is the number of individuals within each cluster.

f

Effect size. It specifies the main effect of treatment, the mean difference between the treatment clusters/sites and the control clusters/sites. Effect size must be positive.

J

Number of clusters / sites. It tells how many clusters are considered in the study design. At least two clusters are required.

tau00

Variance of cluster/site means. It is one of the residual variances in the second level. Its value must be positive.

tau11

Variance of treatment effects across sites. It is one of the residual variances in the second level. Its value must be positive.

sg2

Level-one error Variance. The residual variance in the first level.

power

Statistical power.

alpha

significance level chosed for the test. It equals 0.05 by default.

alternative

Type of the alternative hypothesis ("two.sided" or "one.sided"). The default is "two.sided". The option "one.sided" can be either "less" or "greater".

type

Type of effect ("main" or "site" or "variance") with "main" as default. The type "main" tests treatment main effect, no tau00 needed; Type "site" tests the variance of cluster/site means, no tau11 or f needed; and Type "variance" tests variance of treatment effects, no tau00 or f needed.

interval

A vector containing the end-points of the interval to be searched for the root.

Value

An object of the power analysis.

References

Liu, X. S. (2013). Statistical power analysis for the social and behavioral sciences: basic and advanced techniques. Routledge.

Raudenbush, S. W. (1997). Statistical analysis and optimal design for cluster randomized trials. Psychological Methods, 2(2), 173.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

Examples

#To calculate the statistical power given sample size and effect size:
#For main effect
wp.mrt2arm(n = 45, f = 0.5, J = 20, tau11 = 0.5,
            sg2 = 1.25, alpha = 0.05, power = NULL)
#  Power analysis for Multileve model Multisite randomized trials with 2 arms
#
#      J  n   f tau11  sg2     power alpha
#      20 45 0.5   0.5 1.25 0.8583253  0.05
#
#  NOTE: n is the number of subjects per cluster
#  URL: http://psychstat.org/mrt2arm

#For variance of treament effect
wp.mrt2arm(n = 45, f = 0.5, J = 20, tau11 = 0.5,
               sg2 = 1.25, alpha = 0.05, power = NULL, type = "variance")
#  Power analysis for Multileve model Multisite randomized trials with 2 arms
#
#     J  n   f tau11  sg2     power alpha
#    20 45 0.5   0.5 1.25 0.9987823  0.05
#
#  NOTE: n is the number of subjects per cluster
#  URL: http://psychstat.org/mrt2arm

#For testing site variablity
res<- wp.mrt2arm(n = 45, J = 20, tau00 = 0.5,
                 sg2 = 1.25, alpha = 0.05, power = NULL, type = "site")
#  Power analysis for Multileve model Multisite randomized trials with 2 arms
#
#     J  n tau00  sg2     power alpha
#    20 45   0.5 1.25 0.9999999  0.05
#
#  NOTE: n is the number of subjects per cluster
#  URL: http://psychstat.org/mrt2arm

#To generate a power curve given a sequence of sample sizes:
res <- wp.mrt2arm(n = seq(10,50,5), f = 0.5, J = 20, tau11 = 0.5,
                          sg2 = 1.25, alpha = 0.05, power = NULL)
#  Power analysis for Multileve model Multisite randomized trials with 2 arms
#
#      J  n   f tau11  sg2     power alpha
#     20 10 0.5   0.5 1.25 0.6599499  0.05
#     20 15 0.5   0.5 1.25 0.7383281  0.05
#     20 20 0.5   0.5 1.25 0.7818294  0.05
#     20 25 0.5   0.5 1.25 0.8090084  0.05
#     20 30 0.5   0.5 1.25 0.8274288  0.05
#     20 35 0.5   0.5 1.25 0.8406659  0.05
#     20 40 0.5   0.5 1.25 0.8506049  0.05
#     20 45 0.5   0.5 1.25 0.8583253  0.05
#     20 50 0.5   0.5 1.25 0.8644864  0.05
#
#  NOTE: n is the number of subjects per cluster
#  URL: http://psychstat.org/mrt2arm

#To plot the power curve:
plot(res) 

#To calculate the required sample size given power and effect size:
wp.mrt2arm(n = NULL, f = 0.5, J = 20, tau11 = 0.5,
                      sg2 = 1.25, alpha = 0.05, power = 0.8)
#  Power analysis for Multileve model Multisite randomized trials with 2 arms
#
#     J        n   f tau11  sg2 power alpha
#    20 23.10086 0.5   0.5 1.25   0.8  0.05
#
#  NOTE: n is the number of subjects per cluster
#  URL: http://psychstat.org/mrt2arm